Non-differentiable variational principles

We develop a calculus of variations for functionals which are defined on a set of non differentiable curves. We first extend the classical differential calculus in a quantum calculus, which allows us to define a complex operator, called the scale derivative, which is the non differentiable analogue of the classical derivative. We then define the notion of extremals for our functionals and obtain a characterization in term of a generalized Euler-Lagrange equation. We finally prove that solutions of the Schr\"odinger equation can be obtained as extremals of a non differentiable variational principle, leading to an extended Hamilton's principle of least action for quantum mechanics. We compare this approach with the scale relativity theory of Nottale, which assumes a fractal structure of space-time.Comment: 20 page

Pharmacointeraction Network Models Predict Unknown Drug-Drug Interactions

Drug-drug interactions (DDIs) can lead to serious and potentially lethal adverse events. In recent years, several drugs have been withdrawn from the market due to interaction-related adverse events (AEs). Current methods for detecting DDIs rely on the accumulation of sufficient clinical evidence in the post-market stage – a lengthy process that often takes years, during which time numerous patients may suffer from the adverse effects of the DDI. Detection methods are further hindered by the extremely large combinatoric space of possible drug-drug-AE combinations. There is therefore a practical need for predictive tools that can identify potential DDIs years in advance, enabling drug safety professionals to better prioritize their limited investigative resources and take appropriate regulatory action. To meet this need, we describe Predictive Pharmacointeraction Networks (PPINs) – a novel approach that predicts unknown DDIs by exploiting the network structure of all known DDIs, together with other intrinsic and taxonomic properties of drugs and AEs. We constructed an 856-drug DDI network from a 2009 snapshot of a widely-used drug safety database, and used it to develop PPIN models for predicting future DDIs. We compared the DDIs predicted based solely on these 2009 data, with newly reported DDIs that appeared in a 2012 snapshot of the same database. Using a standard multivariate approach to combine predictors, the PPIN model achieved an AUROC (area under the receiver operating characteristic curve) of 0.81 with a sensitivity of 48% given a specificity of 90%. An analysis of DDIs by severity level revealed that the model was most effective for predicting “contraindicated” DDIs (AUROC = 0.92) and less effective for “minor” DDIs (AUROC = 0.63). These results indicate that network based methods can be useful for predicting unknown drug-drug interactions

Do Remuneration Committees at UK Corporate Banks Exploit the use of Compensation Peer Groups as a Mechanism to Inflate CEO Pay?

Executive compensation within banking has received much attention from academics, politicians, the media and the general public in the light of the recent financial crisis whereby many financial institutions’ market capitalisation has fallen dramatically whilst their CEO’s remain to walk away with large remuneration packages. Although pay arrangements are being scrutinized by these wider commentators to a greater degree, no consensus on the underlying reasons explaining an apparent disconnect between bank performance and CEO pay has been reached. The use of compensation peer groups as a mechanism to allocate pay is widespread across many industries, including banking. Many academics have looked at the effectiveness of compensation peer groups, however the work is predominantly US based and this paper seeks to be the first to look specifically at the UK’s largest corporate banks from 2004-2011. Using a completely original data set collected manually through Annual Reports alongside Datastream and Bankscope, an attempt has been made to test whether the remuneration committees at the UK’s 10 largest corporate banks have been using peer groups as a way to exploit rising pay levels, or whether they are genuinely being used as an effective method to assess CEO performance. Using the Total Shareholder Return performance for the sample of 10 banks, as well as the Total Return Index for the Global FTSE and UK FTSE bank indexes, a multiple linear regression model has been able to test peer group strength following peer movements over the period. The results indicate that across our sample peer movements actually increased peer group strength in comparison to the rest of the market, indicating that remuneration committees have made sound judgements with regards to the composition of compensation peer groups, hence no evidence of manipulation being found. Keywords: Executive Compensation, Remuneration Committees, Compensation Peer Groups, Optimal Contracting Model, Managerial Power Hypothesi

A systematic study of direct photon production in heavy ion collisions

A theoretical derivation of photon bremsstrahlung, induced by the interactions of an energetic quark in a hot and dense quark-gluon plasma, is given in the framework of the reaction operator approach. For the physically relevant case of hard jet production, followed by few in-medium interactions, we find that the Landau-Pomeranchuk-Migdal suppression of the bremsstrahlung photon intensity is much stronger than in the previously discussed limit of on-shell quarks and a large number of soft scatterings. We present the first systematic study of direct photon production in minimum bias d+Cu and d+Au and central Cu+Cu and Au+Au heavy ion collisions at the Relativistic Heavy Ion Collider at center of mass energies of 62.4 GeV and 200 GeV. We find that the contribution of the final-state photon production at pT < 5 GeV is limited to 35%, and at high transverse momenta, the modification of the direct photon cross section is dominated by initial-state cold nuclear matter effects.Comment: Final version published in PLB. Added comments, 2 references and discussion in relation to SDIS observable

A study on the anomaly of pp over π\pi ratios in Au+AuAu+Au collisions with jet quenching

The ratios of $p/\pi$ at large transverse momentum in central $Au+Au$ collisions at RHIC are studied in the framework of jet quenching based on a next-to-leading order pQCD parton model. It is shown that theoretical calculations with a gluon energy loss larger than the quark energy loss will naturally lead to a smaller $p/\pi$ ratios at large transverse momentum in $Au+Au$ collisions than those in $p+p$ collisions at the same energy. Scenarios with equal energy losses for gluons and quarks and a strong jet conversion are both explored and it is demonstrated in both scenarios $p/\pi$ ratios at high $p_T$ in central $Au+Au$ collisions are enhanced and the calculated ratios of protons over pions approach to the experimental measurements. However, ${\bar p}/p$ in the latter scenario is found to fit data better than that in the former scenario.Comment: 20 pages, 13 figures; revised version; accepted for publication in Journal of Physics

On the Role of Global Warming on the Statistics of Record-Breaking Temperatures

We theoretically study long-term trends in the statistics of record-breaking daily temperatures and validate these predictions using Monte Carlo simulations and data from the city of Philadelphia, for which 126 years of daily temperature data is available. Using extreme statistics, we derive the number and the magnitude of record temperature events, based on the observed Gaussian daily temperatures distribution in Philadelphia, as a function of the number of elapsed years from the start of the data. We further consider the case of global warming, where the mean temperature systematically increases with time. We argue that the current warming rate is insufficient to measurably influence the frequency of record temperature events over the time range of the observations, a conclusion that is supported by numerical simulations and the Philadelphia temperature data.Comment: 11 pages, 6 figures, 2-column revtex4 format. For submission to Journal of Climate. Revised version has some new results and some errors corrected. Reformatted for Journal of Climate. Second revision has an added reference. In the third revision one sentence that explains the simulations is reworded for clarity. New revision 10/3/06 has considerable additions and new results. Revision on 11/8/06 contains a number of minor corrections and is the version that will appear in Phys. Rev.